Q: Which equation correctly converts Cartesian coordinates (x, y) to polar coordinates (r, \theta)?

$$r = \sqrt{x^2$ + y^2$}$$ and $$\theta = \tan$$^{-1}$$(y/x)$$

Q: Which of the following is the correct expression for the tangent of an angle in a right triangle, as shown in the sixth image?

$$\tan \theta = \frac{\text{opposite side}}{\text{adjacent side}}$$

Q: Given a point in polar coordinates $$(r, \theta)$$, which equations convert it to Cartesian coordinates $$(x, y)$$?

$$x = r \cos \theta$$, $$y = r \sin \theta$$

Q: A person measures the height of a building by walking 46.0 m from its base and shining a flashlight at an angle of 39.0°. If the flashlight is held at a height of 2.00 m, what is the height of the building?

$$h = 46.0 \times \tan 39.0^\circ + 2.00$$

Q: Convert 90 km/h to m/s using unit conversion. Which calculation is correct?

$$90 \times \frac{1000}{3600}$$

Question 1

Which of the following best describes the purpose of the International Prototype of the Kilogram, as shown in the first image?

Accepted Answer

It serves as the standard reference for the unit of mass in the SI system.

Question 2

The second image shows a cesium fountain atomic clock. According to the SI definition, how is the second defined?

Accepted Answer

As 9,192,632,700 periods of oscillation of radiation from the cesium atom.

Question 3

In the Cartesian coordinate system shown in the third image, what are the coordinates of point Q?

Accepted Answer

(-3, 4)

Question 4

Which equation correctly converts Cartesian coordinates (x, y) to polar coordinates (r, 	heta)?

Accepted Answer

$$r = \sqrt{x^2$ + y^2$}$$ and $$	heta = 	an$$^{-1}$$(y/x)$$

Question 5

Refer to the fifth image (Table 1.4). What is the correct prefix and abbreviation for $$10^{-6}$$?

Accepted Answer

micro, \mu

Question 6

Which of the following is the correct expression for the tangent of an angle in a right triangle, as shown in the sixth image?

Accepted Answer

$$	an 	heta = \frac{	ext{opposite side}}{	ext{adjacent side}}$$

Question 7

Given a point in polar coordinates $$(r, 	heta)$$, which equations convert it to Cartesian coordinates $$(x, y)$$?

Accepted Answer

$$x = r \cos 	heta$$, $$y = r \sin 	heta$$

Question 8

A person measures the height of a building by walking 46.0 m from its base and shining a flashlight at an angle of 39.0°. If the flashlight is held at a height of 2.00 m, what is the height of the building?

Accepted Answer

$$h = 46.0 	imes 	an 39.0^\circ + 2.00$$

Question 9

If the length of the light beam in the previous scenario is to be calculated, which equation would you use?

Accepted Answer

$$r = \frac{46.0}{\cos 39.0^\circ}$$

Question 10

Which of the following is NOT a fundamental SI unit?

Accepted Answer

joule

Question 11

A measurement is recorded as 0.00340 m. How many significant figures does this value have?

Accepted Answer

3

Question 12

Convert 90 km/h to m/s using unit conversion. Which calculation is correct?

Accepted Answer

$$90 	imes \frac{1000}{3600}$$

Question 13

Which of the following statements about dimensional analysis is correct?

Accepted Answer

Both sides of an equation must have the same dimensions.

Question 14

When multiplying or dividing measured quantities, how should the number of significant figures in the result be determined?

Accepted Answer

It should match the number of significant figures in the least accurate factor.

Question 15

Which prefix corresponds to $$10^{12} in $$the metric system?

Accepted Answer

tera (T)

Question 16

If you add 3.45 m and 2.1 m, how should you report the result according to significant figure rules?

Accepted Answer

5.6 m

Question 17

Which coordinate system is best for describing the position of a point relative to a distance and angle from a reference line?

Accepted Answer

Plane polar coordinate system

Question 18

What is the order of magnitude of the number 4,500,000?

Accepted Answer

$$10^6$$

Question 19

Which of the following is a correct statement about uncertainty in measurements?

Accepted Answer

Uncertainty carries over through calculations and must be accounted for.

Chapter 1: Representing Motion – Structured Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards